Question

A spherical shell 5 m thick has an outer radius of 7 m. What is the volume of shell?

• A. $1202.53m$
• B. $1302.53m$
• C. $1402.53m$
• D. $1102.53m$

Answer 1

Answer: (C)

$1402.53m$

Thickness, $T=R-r$
$5=7-r$
$r=7-5=2$ m
$R=7$ m
Volume = $\frac{4}{3}\pi (R^3-r^3)$
= $\frac{4}{3}\pi (7^3-2^3)$
= $\frac{4}{3}\pi (343-8)$
= $\frac{4}{3}\pi \left(335\right)$
= $\frac{1340\pi }{3}$
= $1402.53m$